As far as temporary vehicle registration number is concerned, it is valid only until the permanent number is issued. The validity of the temporary number is around one month. Within this period the owner of the vehicle needs to fill up form 20 at the Regional transport office under whose jurisdiction the address of the owner falls. A vehicle with temporary registration should not leave the state.
If an owner does not get the permanent number registered within one month, then it would attract a fine.
So, please contact the owner from whom you have purchased the vehicle. Then, approach the RTO office for the application of the permanent registration number. There would be a fine, that can be paid by the previous owner. Then once the RTO records are in order and the permanent number is entered, the previous owner has to contact the Insurance provider to updated vehicle details. When there is such a major change, the insurance provider might insist on examining the vehicle by their own authorities.
After getting the correct updated valid insurance policy document, then you can proceed to change the name. You need to have the transfer of ownership form 29 with the relevant documents. The time taken for vehicle ownership transfer is around 3-4 weeks. I would suggest you get in touch with the seller soon and get these certifications sorted out. If still not clear, please approach the RTO authorities they would certainly guide you both.